Question

Water is flowing continuously from a tap having an internal diameter $8\times 10^{-3}m$. The water velocity as it leaves the tap is $0.4m{s}^{-1}$. The diameter of the water stream at a distance $2\times 10^{-1}m$ below the tap is close to

• A. $5.0\times 10^{-3}m$
• B. $7.5\times 10^{-3}m$
• C. $9.6\times 10^{-3}m$
• D. $3.6\times 10^{-3}m$

Answer 1

Answer: (D)

Here, $d_1=8\times 10^{-3}m$,
$v_1=0.4m{s}^{-1},h=0.2m$
According to equation of motion,

$v_2=\sqrt{v_1^2+2gh}=\sqrt{{\left(0.4\right)}^2+2\times 10\times 0.2}$
$\approx 2m{s}^{-1}$
According to equation of continuity, $A_1{v}_1=A_2{v}_2$
$\therefore \pi \times {\left(\frac{8\times 10^{-3}}{2}\right)}^2\times 0.4=\pi \times {\left(\frac{d_2}{2}\right)}^2\times 2$
or $d_2=3.6\times 10^{-3}m$